Given, the number of bacteria doubles every hour. Hence, the number of bacteria after every hour will form a G.P.

Here we have, a = 30 and r = 2

So, a_{3} = ar^{2} = (30) (2)^{2} = 120

Thus, the number of bacteria at the end of 2^{nd} hour will be 120.

And, a_{5} = ar^{4} = (30) (2)^{4} = 480

The number of bacteria at the end of 4^{th} hour will be 480.

a_{n +1 }= ar^{n} = (30) 2^{n}

Therefore, the number of bacteria at the end of n^{th} hour will be 30(2)^{n}.

Construct a quadratic in x such that A.M. of its roots is A and G.M. is G.

Find the geometric means of the following pairs of numbers:

**(i) **2 and 8

**(ii) **a^{3}b and ab^{3}

**(iii) **–8 and –2

Insert 5 geometric means between \( \dfrac{32}{9}\) and \( \dfrac{81}{2}\).